Analysis of the dynamical behavior of a feedback auto-associative memory

The dynamical behavior and the stability properties of fixed points in a feedback auto-associative memory are investigated. The proposed structure encompasses a multi-layer perceptron (MLP) and a feedback connection that links input and output layers through delay elements. The MLP is initially trained so that it maps the training patterns into themselves as an auto-associative memory. The feedback connection is then established in order to make the feedback auto-associative memory. We derive some explicit equations based on the theory of dynamical systems, which relate the stability properties of fixed points to the network parameter values. We then perform some case studies for the purpose of performance comparisons between the proposed model and a self-feedback neural network (SFNN) as an associative memory. Several simulations are provided to verify that not only our model needs much fewer neurons to store numerous stable fixed points, but also it is able to learn asymmetric arrangement of fixed points, whereas the SFNN model is limited to orthogonal arrangements.